Skip to main content

Advertisement

SpringerLink
Log in

Energy spread and current-current correlation in quantum systems

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We consider energy (heat) transport in quantum systems, and establish a relationship between energy spread and energy current-current correlation function within linear response theory. The energy current-current correlation is related to thermal conductivity by the Green-Kubo formula, and thus this relationship allows us to extract heat conductivity from the energy spread process. As an example, we investigate a spinless fermion model. At high temperatures, we find good agreement between numerical results and theory. At low temperatures and for finite systems, boundary terms however need to be taken into account due to the finite-size effect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, B. Li, Rev. Mod. Phys. 84, 1045 (2012)

    Article  ADS  Google Scholar 

  2. S. Lepri, R. Livi, A. Politi, Phys. Rep. 377, 1 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Dhar, Adv. Phys. 57, 457 (2008)

    Article  ADS  Google Scholar 

  4. S. Liu, X.F. Xu, R.G. Xie, G. Zhang, B. Li, Eur. Phys. J. B 85, 337 (2013)

    Article  ADS  Google Scholar 

  5. X. Zotos, P. Prelovšek, in Strong Interactions in Low Dimensions (Kluwer Academic Publishers, Dordrecht, 2004), Chap. 11

  6. E. Helfand, Phys. Rev. 119, 1 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Viscardy, J. Servantie, P. Gaspard, J. Chem. Phys. 126, 184513 (2007)

    Article  ADS  Google Scholar 

  8. S. Denisov, J. Klafter, M. Urbakh, Phys. Rev. Lett. 91, 194301 (2003)

    Article  ADS  Google Scholar 

  9. B. Li, J. Wang, L. Wang, G. Zhang, Chaos 15, 015121 (2005)

    Article  ADS  Google Scholar 

  10. H. Zhao, Phys. Rev. Lett. 96, 140602 (2006)

    Article  ADS  Google Scholar 

  11. V. Zaburdaev, S. Denisov, P. Hänggi, Phys. Rev. Lett. 106, 180601 (2011)

    Article  ADS  Google Scholar 

  12. A. Dhar, K. Saito, B. Derrida, Phys. Rev. E 87, 010103 (2013)

    Article  ADS  Google Scholar 

  13. Y. Li, S. Liu, N. Li, P. Hänggi, B. Li, arXiv:1407.1161v1 (2014)

  14. S. Liu, P. Hänggi, N. Li, J. Ren, B. Li, Phys. Rev. Lett. 112, 040601 (2014), and the supplementary material

    Article  ADS  Google Scholar 

  15. P. Cipriani, S. Denisov, A. Politi, Phys. Rev. Lett. 94, 244301 (2005)

    Article  ADS  Google Scholar 

  16. N. Li, B. Li, S. Flach, Phys. Rev. Lett. 105, 054102 (2010)

    Article  ADS  Google Scholar 

  17. X. Zotos, P. Prelovšek, Phys. Rev. B 53, 983 (1996)

    Article  ADS  Google Scholar 

  18. X. Zotos, Phys. Rev. Lett. 82, 1764 (1999)

    Article  ADS  Google Scholar 

  19. B.N. Narozhny, A.J. Millis, N. Andrei, Phys. Rev. B 58, R2921 (1998)

    Article  ADS  Google Scholar 

  20. F. Heidrich-Meisner, A. Honecker, D.C. Cabra, W. Brenig, Phys. Rev. B 68, 134436 (2003)

    Article  ADS  Google Scholar 

  21. J. Benz, T. Fukui, A. Klümper, C. Scheeren, J. Phys. Soc. Jpn Suppl. 74, 181 (2005)

    Article  ADS  Google Scholar 

  22. C. Karrasch, J.H. Bardarson, J.E. Moore, Phys. Rev. Lett. 108, 227206 (2012)

    Article  ADS  Google Scholar 

  23. X. Zotos, Phys. Rev. Lett. 92, 067202 (2004)

    Article  ADS  Google Scholar 

  24. P. Jung, A. Rosch, Phys. Rev. B 76, 245108 (2007)

    Article  ADS  Google Scholar 

  25. C. Karrasch, R. Ilan, J.E. Moore, Phys. Rev. B 88, 195129 (2013)

    Article  ADS  Google Scholar 

  26. M. Žnidarič, Phys. Rev. Lett. 110, 070602 (2013)

    Article  Google Scholar 

  27. M. Montagnese et al., Phys. Rev. Lett. 110, 147206 (2013)

    Article  ADS  Google Scholar 

  28. M. Otter et al., Int. J. Heat Mass Transfer 55, 2531 (2012)

    Article  Google Scholar 

  29. M. Otter et al., J. Magn. Magn. Mater. 321, 796 (2009)

    Article  ADS  Google Scholar 

  30. X. Zotos, F. Naef, P. Prelovšek, Phys. Rev. B 55, 11029 (1997)

    Article  ADS  Google Scholar 

  31. A. Klümper, K. Sakai, J. Phys. A 35, 2173 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. C. Karrasch, J.E. Moore, F. Heidrich-Meisner, Phys. Rev. B 89, 075139 (2014)

    Article  ADS  Google Scholar 

  33. M. Michel, G. Mahler, J. Gemmer, Phys. Rev. Lett. 95, 180602 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. S. Langer, F. Heidrich-Meisner, J. Gemmer, I.P. McCulloch, U. Schollwöck, Phys. Rev. B 79, 214409 (2009)

    Article  ADS  Google Scholar 

  35. S. Langer, M. Heyl, I.P. McCulloch, F. Heidrich-Meisner, Phys. Rev. B 84, 205115 (2011)

    Article  ADS  Google Scholar 

  36. R. Steinigeweg, J. Gemmer, Phys. Rev. B 80, 184402 (2009)

    Article  ADS  Google Scholar 

  37. R. Steinigeweg, H. Wichterich, J. Gemmer, Europhys. Lett. 88, 10004 (2009)

    Article  ADS  Google Scholar 

  38. G.D. Mahan, in Many-particles Physics (Plenum Press, New York, 1990), Chap. 3

  39. J. Gemmer, R. Steinigeweg, M. Michel, Phys. Rev. B 73, 104302 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Shaoxing University, Shaoxing, 312000, P.R. China

    Yonghong Yan

  2. School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, P.R. China

    Feng Jiang

  3. Key Laboratory for Advanced Microstructure Materials of the Ministry of Education and Department of Physics, Tongji University, Shanghai, 200092, P.R. China

    Hui Zhao

Authors
  1. Yonghong Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonghong Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, Y., Jiang, F. & Zhao, H. Energy spread and current-current correlation in quantum systems. Eur. Phys. J. B 88, 11 (2015). https://doi.org/10.1140/epjb/e2014-50797-4

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50797-4

Keywords

Search

Navigation